Linear range of analog audio volume pot (variable resistor)

[13hm13]

I'm referring to the the common analog volume control found in audio circuits ...

All else being equal, where in its full range (say, 0-100) is it most "linear"? So, where in its range (e.g., 0-49 or 50-100) does the volume control distort the audio signal least?

Some factors that may be worth considering:

Resistance in the audio path is a nemesis, so "high end" volume control can take great lengths to attempt lower distortion...e.g....

I have read from a few sources that the higher end (50-100) may be "cleaner" -- assuming the higher the volume, the less resistance material the audio signal will pass thru (??)

Another factor to consider may be impedance matching to the stage preceding or following the volume control. When you vary the vaiable resistance, you inevitably affect the total impedance of the immediate circuit its in.

Any input is appreciated -- thanks!!

[AG6QR]

The common use of the term "linear" regarding a potentiometer refers to the idea of the resistance being a linear function of the angular position of the knob.  In a perfect linear pot, a graph of the resistance versus angle ought to be a perfectly straight line.

But I don't think you're talking about that kind of linearity here.  For one thing, volume controls are rarely linear taper.  Furthermore, the above sense of linearity is unimportant to sound quality -- it only affects the user's ability to precisely control the volume using the volume control across the full range of the volume pot.

I'm not entirely sure what kind of linearity you ARE referring to, but I think you're talking about when the pot most closely resembles an ideal resistor?  That is, when its resistance is most nearly constant, across all frequencies, with negligible capacitance and inductance, and the lowest possible noise?

Or are you talking about something else being linear?  When you say "linear", what exactly are the axes of the graph where you'd like to see that perfectly straight line?

Regarding noise, there are different kinds, but some can't be eliminated regardless of the resistor technology.

http://www.analog.com/en/content/raq_lownoiseamp/fca.html

[13hm13]

I forgot to note that there is also present the phenomenon known as Johnson-Nyquist noise.
http://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/iandm/part3/page1.html

[13hm13]

The common use of the term "linear" ....

Answer to my use of "linear" in as many ways as possible (as you somewhat have).
WRT human hearing and volume, it's a different issue due to Fletcher-Munson effect:
http://en.wikipedia.org/wiki/Fletcher%E2%80%93Munson_curves

[linux-works]

the question makes no sense to me, sorry.

are you talking about left/right stereo tracking?  on analog pots, tracking gets bad as you reach higher atten (lower output levels).  on steppers like you pictured, they are matched left and right and so they don't vary much at all and the l/r balance stays perfect.  db steps also are perfect with steppers.

I designed a relay based stepper (amb.org delta1) and have some experience with this subject matter.

a lot of the performance depends on post-buffering after the vol control and possibly pre-buffering, if the source is very far away or high output-z.

but with steppers, either manual, like your photo or relay based, there is no 'sweet spot'.  the buffer AFTER it would have various regions where it starts to clip and where it starts to have too much low level noise.  but atten stage, though, does not affect this in any real way.

[linux-works]

Another factor to consider may be impedance matching to the stage preceding or following the volume control. When you vary the vaiable resistance, you inevitably affect the total impedance of the immediate circuit its in.

and that's one huge reason why you have an atten first, then a buffer after that, optionally with gain.  after the buffer, you are low-z again and life is good   you never want to run cables from the atten - for very long distances - unbuffered.  the high output z is very bad and noise WILL get in.

[Hideki]

A lower output level or high impedance gets you closer to the noise floor and may let external interference in, but noise is not the same as nonlinearity.

The common analog volume control (assuming you mean only the potentiometer and not the entire surrounding circuit) doesn't really distort much at all. Maybe an oxidized track could form some kind of nonlinearity at the point where the wiper connects to it, but I think a normal pot would be mostly undetectable on a distortion analyzer.

If you really want to know, measure it. Or, since you are unlikely to have the right equipment, get someone to measure it for you.

Common thick-film smd resistors are probably more nonlinear. See for example Small Signal Audio Design by Douglas Self.

Please don't call those curves the "Fletcher-Munson effect". They are, as the web page says, equal-loudness contours. They have been updated a few times since Fletcher and Munson first measured them, and the current standard is ISO 226:2003. I fail to see how they are connected to your question.

[13hm13]

and that's one huge reason why you have an atten first, then a buffer after that, optionally with gain.  after the buffer, you are low-z again and life is good   you never want to run cables from the atten - for very long distances - unbuffered.  the high output z is very bad and noise WILL get in.

linux-works ... what a coinkidink .... My query for this thread mostly arose as a result of building myriad headphone amps -- CMoy, Tangent/Pi Meta, etc. -- so perhaps you're best suited to pontificate*** your usual excreta
=== !!WARNING!! -- SUBJECTIVE AUDIO EVALUATION BELOW. SAVE THE UBIQUITOUS  "AUDIOPHILE"-BASHING MELODRAMA FOR THOSE WHOSE SINGLE PREAMP VACUUM TUBE COSTS MORE THAN MY WHOLE AUDIO SYSTEM !! ===

Setting my DAP's ( a cheap $100 Chinese "iPod") volume to about 1/2 level [it operates in the digital domain, via the DAC], I am "forced" to use the entire range of my DIY PiMeta headphone amp's rotary (analog) volume control -- the max setting (five o'clock) being just at maximum tolerable level. To confirm, quantitatively, I level matched the headphone amps output voltage, with a DMM.
Qualitatively, I noted a distinct improvement in subjective audio quality -- i.e., when compared against the same voltage level with the DAP volume higher** (100%) and the headphone-amp (rotary analog) lower.

Dunno where I got the idea to test this ... maybe years or even decade ago there was some mention of it in Audio Engineering magazine ... or was it now long-out-of print High Fidelity
Anyway, it's an easy test for ANYONE to perform ... and most of you (even the most unaudiophile of the bunch) probably have orders of magnitude more invested in common/household audio gear than yours truly
HINT: There's a reason I'm headphones only ... speakers are way too $$.

** The DAP in question has both headphone out and line out jacks. The digital volume control operates both. Most recommendations I've read -- WRT using the line-out with an external amp -- suggest one max out the source (DAP) volume. But this is not what I find works best for subjective eval. of audio fidelity. YMMV.

*** "pontificate" ? ... or is that defecate  ??
 

[Phaedrus]

The common use of the term "linear" ....

Answer to my use of "linear" in as many ways as possible (as you somewhat have).

Unfortunately, things don't really work that way. You can't simply say you want something to be "linear" without having an agreement on what linear means. You need to find the property relationships of your resistor that matter most (eg. R/°rotation, Z/°rotation, Z/F, Z/T, noise/T, noise/F, etc.), define what your acceptable or target range is, then we can give you a proper answer. Because that's how engineering actually works.

I suspect, however, that you may be a victim of audiowank.

[13hm13]

I suspect, however, that you may be a victim of audiowank.

Of course I am

[linux-works]

short answer: you almost never want to attenuate digitally and prefer to do it analog wise.

digital atten often means bit shaving.  or you do a full resample and redither and most dacs and processors don't do that.  you also have to do the atten at 32 bits for digital to sound as good as analog attens.

that's why its always recommended to run dacs at 0db (no atten) and then use a buffer stage or preamp do add gain where needed, but mostly to attenuate.  when in atten mode, there should not be any noise or distortion in a well designed system (I've built my share of pimetas, too).

what you have to care about are 2 things: noise level for low volume songs or sources; and clipping for when the output is too much for the next buffer stage.  none of that is any fault of the vol control, itself.  the vol control itself add nearly no noise or distortion of its own.  pots do have rolloffs as you get closer to the higher atten settings (resistance and capacitance get you) but on steppers, you usually are pretty clean way beyond audio cutoff freq's.

[linux-works]

one more thing that is relevant: gain levels.

driving earbuds is not the same work as driving hd650 (etc).  you do need to carefully pick the gain level of the amp or you will have more 'room' on the pot than you need (and a worse noise figure); or you won't have enough drive and it won't play loud enough.

sometimes it even make sense to have switchable gain settings.

a smart volume control can do both; it can be an attenuator and also switch in or out stages or gain setting values.  that way you really can have a 'one size fits all' vol control system.

[13hm13]

that's why its always recommended to run dacs at 0db (no atten) and then use a buffer stage or preamp do add gain where needed, but mostly to attenuate.  when in atten mode, there should not be any noise or distortion in a well designed system (I've built my share of pimetas, too).

With the Colorfly CK-4 DAP, I have NO CHOICE -- the LO and HO are BOTH affected by the digital vol. control.
But this isn't actually too bad as the CK-4 sounds better than many similar-$ DAP (Teclast, Fiio, etc) that have pure LO.

I thought the CK4 LO's "forced" atten. was a curse. But accidentally (serendipitously, in fact) I'd one day forgotten to turn it's vol. all the way up to max for LO use (I'd been using the CK-4's HO directly as my PiMeta was not avail.) ....anyway, after a few minutes of listening with the PiMeta, I'd begun to notice music/audio details that were not as audible previously.  --you know, the subjective kind that get many of us labeled as "audio-wanks", etc., via the usual unexamined pejoratives and drivel that the non-audio "EE" community defecates with.

For the CK4 DAP, I think I settled at 2/3 level (66%) as best.

Can't remember where but I've encountered the same 2/3 suggestions for setting PC audio-card volume. My PC's Asus Xonar audio card is connected to a PPA2 headphone amp. Setting the audio card volume lower forces me to use the full range of PPA2. Yes, I do think digital vol. controls degrade sound a tiny bit ... but IMO it's more than made up for with the phenomenon I'm noticing/claiming.

[linux-works]

you don't have the gain settings correct, then.  your whole chain, I mean.

if you find yourself needing to atten at the dac level, things are wrong.  your amp chain is set too high for too much gain structure.

ideally, your dac should output 100% signal (no atten at all) and the rest of the chain should allow a fullscale vol control knob (at max) to JUST play about as loud as you can take it.  if you're not using most of the vol control range, then your gain structure is not optimal or its trying to support too many load Z levels.

when you run the digital vol control at less than 100%, you are removing bits from the effective resolution and so it makes sense that you'd hear 'more music' if you avoid digital attenuation.

[13hm13]

ideally, your dac should output 100% signal (no atten at all

Yes, I'd always thought so ... what I don't know is where in it's graphical display (range) "100%" ACTUALLY is???
For all I know, at the max DISPLAYED level, the volume may electrically/topologically be 150%.

BTW:
The 2/3 level was also noted for a California Audio Labs CL-15 CD player, in this 1998 Stereophile review:

Volume control is implemented in the digital domain, so it doesn't change the analog gain but rather the digital-to-analog scaling. According to CAL, reducing the volume won't result in a loss of resolution as long as the CL-15 is operated in the top two-thirds of its output range, with less than 18dB of attenuation.

[13hm13]

... if you're not using most of the vol control range, then your gain structure is not optimal or its trying to support too many load Z levels.

Unrelated somewhat to my orig. query, this is a noteworthy comment... and another reason why the absurd "loudness-war" -era CDs (and, now, hyperloud music streams and downloads) are a compromise. Pre-loudness-era CDs sound better for THIS and other reasons

Refs:
http://en.wikipedia.org/wiki/Loudness_war

[linux-works]

btw, this is the delta1 that I designed and my friend 'amb' sells:



you have 8 relays and you can pick your step size and relay count up thru 8.  typically people go for 127db, 8 relays and half db step size.  a half db is a nice little 'nudge' if you want to bump things up or down a bit.  my firmware (that runs on the controller called the LCDuino) lets you vary volume by native half-db steps or user-defined 'big steps'.  I have the big-step size set to 3.5db for my own preamps and that's about right to take large strides if you need to make big changes.

127db is a lot of range.  but even if you only use a bit of it, its still 'all linear' and it does not matter that you are 'wasting' range.  I've done lots and lots of tests on this and its flat to the mhz range.  there's no loss to audio thru this atten and all the 'problems' would be from any buffer stages that come after.

[13hm13]

btw, this is the delta1 that I designed and my friend 'amb' sells:

Nice ... but careful around here ... you get branded by the natives as an audiophile or audiowank. It's the same story: crude dismissal and denigration by the unwashed mass.

[13hm13]

you have 8 relays and you can pick your step size and relay count up thru 8.

Well, to get to the bottom line ... does it take ALL THAT to get the volume SQ to optimize? IOW, why is that not done, in the orig. manuf. topology., in consumer gear? ...  is it too $  -- like in that $100 CK4 DAP (putatively, a high-performance model) and even my $150 "audiophile" Xonar sound card? They are not high-priced by any means.

[Phaedrus]

Actually it has more to do with your vague question using an audiophile catchword, the fact that you based your opinion on a single subjective data point which may or may not be justified, and that you also immediately tried to disclaim being an audiophile before anyone brought it up--"the lady doth protest too much", etc. But it doesn't matter; we're the unwashed masses, right? 

[linux-works]

you have 8 relays and you can pick your step size and relay count up thru 8.

Well, to get to the bottom line ... does it take ALL THAT to get the volume SQ to optimize?

its way too expensive for most manuf's to use.  a 50 cent or cheaper pot can be used if you run audio thru it.  but more these days, its a rotary encoder (very low cost) talking to a cpu that talks to some atten engine (usually a chip that does dsp and other fun things).  they do their atten digitally (most often) but if they do it as normal part of a dsp chain, they usually are at very high word sizes and so the math errors don't accumulate and digital vol control is not horrible.  analog is still better, though.

what I like from the DIY versions is that you get to pick a lot of things and you have a lot of choices.  one of my earlier builds was 7 relays and 1db per step.  1db was great.  usable, simple display (no dots and no digits after the dot) and less noise as the relays chatter.  having half a db is the most I'd want to live with but finding the exact right spot for some songs can make the listening experience better and sometimes that half db is what you want.  I would not recommend going to 1/4 db, that's way too fine.  and again, the half db stuff is just for tweaks; I speed along with my 'big steps' most of the time and then zero-in with the half-db steps.  it works great and its like going from an auto transmission to a stick-shift.  you feel much more in control.

sound wise, its nice to just know that the atten and buffer stage are not hurting things.  you don't want any roll-off, you want equal channel balance, you want repeatable/settable values and for me, I like good feedback in terms of a display or an indicator (bargraph, digits or even motor pot and pointer knob).  finally, you can get remote control for nearly free.

its not all about the sound.  for me, a lot is the UI style and convenience/usability factor.  digitally controlled analog vol controls are the best of all worlds and not hard or expensive to integrate.

[13hm13]

Actually it has more to do with your vague question using an audiophile catchword, the fact that you based your opinion on a single subjective data point which may or may not be justified, and that you also immediately tried to disclaim being an audiophile before anyone brought it up--"the lady doth protest too much", etc. But it doesn't matter; we're the unwashed masses, right? 

I apologize for humiliating you in the company of your non-audiophile majority ;